Rotating-wave rotation detector and method of operating same

ABSTRACT

A bell-like high-Q member having sides capable of being flexed in a radial vibration pattern defining an anti-nodal region that is free to rotate about the sides in proportion to the rotation of the sides about an input axis. A forcer is mounted adjacent and encircling the periphery of the sides and is effective at the instantaneous angular position of the anti-nodal region to parametrically excite and exercise the sides. Sensor means are located adjacent the periphery and along radii fixed with respect to the bell sides to measure the pattern rotation with respect to bell rotation.

[ 1 March 6, 1973 United States Patent Lynch l a m NF m0 D no TH OT E EM V M A M G N ITT CA AER mum RDO 4 D Attorney-E. W. Christen, C. R. Meland and Albert F. Duke [75] Inventor: David D. Lynch, Greendale, Wis.

[73] General [57] ABSTRACT A bell-like high-Q member having sides capable of [22] Filed:

being flexed in a radial vibration pattern defining an [21] PP N04 77,067 anti-nodal region that is free to rotate about the sides in proportion to the rotation of the sides about an 52 us. axisfmer is moPmed adiacem 9 encir- G01C 19/56 clmg the perlphery of the sides and 1s effective at the instantaneous angular position of the anti-nodal region [58] Field of Search to parametrically excite and exercise the sides. Sensor means are located adjacent the periphery and along radii fixed with respect to the bell sides to measure the pattern rotation with respect to bell rotation.

[56] References Cited UNITED STATES PATENTS 3,307,409 Newton, Jr. 8 Claims, 4 Drawing Figures PATENTEUMAR' ems SHEET 10;- 2

OSCILL W CIRC READ-OUT CIRCUITS ATTORNEY PATENTED 6 I975 3, 7 19,0 74 SHEET 2 OF 2 LEVEL AMP 2w FILTER DC DETECTOR & CONVERTER 1 "COMP. II 202 20% 2W REF. 2/2 ADJ. Z/4 %5 I I MULTI- FLIP- OsCILLATOR DEMOD' VIBRATOR FLOP FORCER CIRCUIT I Z 6 Z5? Z5 7 FLIP- MONOSTABLE FLOP PHASE ---Z3? ADJ. ZZZ z,

AIfP. DEMOD.

COME Z26 READ-OUT SUMMING AMP.

Zflfl\ OSCILLATOR RICK-OFF AMPLIFIER INVENTOR.

ATTORN EY ROTATING-WAVE ROTATION DETECTOR AND METHOD OF OPERATING SAME This invention relates to rotation detectors of the type described and claimed in U.S. Pat. applications Ser. No. 843,109, now [1.8. Pat. No. 3,625,067, Ser. No. 863,857, Ser. No. 863,861, and Ser. No. 864,019, respectively entitled Device for Detecting Rotation About An Axis and Method of Using Same (Ser. No. 843,109), Improved Bell Gyro and Method of Making Same (S.N. 863,857), Bell Gyro and Method of Making Same (S.N. 863,861 and "Bell Gyro and Improved Means for Operating Same (S.N. 864,019), the first filed by Alfred G. Emslie on July 18, 1969 and the last three filed by David D. Lynch and Richard E. Denis on Oct. 6, 1969, assigned to the same assignee as the assignee of this application, and incorporated herein by reference.

A bell-like high-Q member may have the sides thereof vibrated by a forcer to establish thereabout a standing-wave vibration pattern defining nodal and anti-nodal regions. Subsequent rotations of a member so vibrated causes vibrations to appear at regions otherwise nodal in the absence of member rotation. These nodal vibrations are of a frequency related to the forcing frequency but of a magnitude varying with input rate. As long as the frequencies along the nodal and anti-nodal axes are substantially the same, i.e., degenerate, and depending on which nodal regions are considered, the vibrations at the nodal and anti-nodal regions add and subtract to comprise a single standing wave that rotates about the input axis. With a constant input rate, constant amplitude vibrations are added and subtracted to the rotating standing wave at its instantaneous nodal regions and the vibration pattern rotates at a constant rate. The greater the input rate, the greater these nodal vibrations, and the fasterthe pattern rotation. Conversely, when the input to the member subsequently terminates, the pattern stops rotating.

The amount of pattern rotation is thus an integration of the magnitude of the input rate over some duration. If the period of integration is some interval substantially less than the duration of input, as with the detector of the above-cited applications, then the amount of pattern rotation corresponds to amount of angular input over that interval, in other words, the input rate. If, on the other hand, the period of integration is over the entire duration of input, as possible with detectors of the present invention, the amount of pattern rotation corresponds to the total input angle by some fraction such as 0.3. The effect of pattern rotation with the present invention is that, as a given radius of the bell (i.e., a bell-referenced radius) is rotated in one direction about the bells input axis, the standing-wave pattern rotates away from that radius in the other direction. Or, viewing this rotation with respect to an axis fixed in inertial space, the effect is that as the bell radius under consideration rotates from the inertially fixed axis at one rate, the standing-wave pattern rotates in the same direction but with lower rate.

Regardless whether viewed from detectorreferenced or inertially-referenced axes, the difference between the rotation of the bell and rotation of the pattern is a function of the bell geometry and the number of nodal regions about its flexed periphery. However, whether the pattern rotates freely about the input axis or not depends primarily on two factors: the Q of the bell, and, if the Q is not infinite, whether the exercising forcer can act along any radius about the bell sides or not. If the Q of the member were substantially infinite, the application of a single exercising pulse would establish a vibration pattern having an indefinite decay time, also known as ringing time. lnput rotation to the member would then result in the substantially-undamped rotation of the standing wave pattern about the input axis as long as there were input. At the termination of hell rotation, the pattern would still be present and its position could be detected to indicate the amount of bell rotation.

However, because of dissipative forces such as irreversible heat flow between adjacent parts of the medium when heating and cooling under periodic stresses, materials having substantially infinite Q's are not known, and most materials having Q's sufficient to establish standing waves for periods of hours or days before re-excitement usually are not sufficiently stable, machinable, or homogenous to establish standingwaves suitable for detection. Thus, the implementation of a bell gyro in a mode requiring the application of a single exciting force not yet being practical, resort is taken to modes permitting the use of materials having reasonably high Qs but requiring the repetitive application of energy to replace that lost by the member in vibration. One form of such repetireplenishment of energy is, as described in the above-cited applications, by a forcer or forcers acting along radii fixed with respect to the bell. And in another form, that of the present invention, the lost energy is also replaced repetitively, but along any radii about the input axis corresponding with the instantaneous position of the anti-nodal axis. This omniazimuth forcing capacibility is provided by a forcer encircling the sides of the bell so as to impart energy of the proper phase with respect to the motion of the sides to an anti-nodal region of the lip in any location of the region about the input axes.

If, as in the above-cited applications, the forcer is effective along any fixed axes, the rotation is retarded so that it appears inhibited. On the other hand, if the forcer is effective to flex the sides along any radius where the anti-nodal axis happens to be, as with the present invention, the pattern can rotate freely. in either event, the angular position of points on this wave can be determined by sensors acting along radii fixed with respect to the bell.

Should the forcer be operative to impart attractive forces along an a axis fixed with respect to the sides, the

position of the anti-nodal axis of the pattern is then a predetermined function of both the position of the forcer and the input rate. Moreover, in this configuration, the vibration pattern is constrained from any further rotation about the input axis other than that proportional to the input rate. This is believed due to the resolution of the flexing forces imparted to the rotating bell continuously along the instantaneous and mathematically-orthogonal modal and anti-nodal axes of the standing wave pattern. Pattern rotation is therefore stopped when that component of the flexing forces or vibrations resolved along the instantaneous nodal axes exactly balances those forces or vibrations produced along the same axes by the effects of the standing wave pattern and the input rotation of the bell.

The amount of pattern rotation, as exhibited by the magnitude of vibrations detected by sensors at regions tern is furthermore substantially inhibited from rotating at all and the magnitude of the nulling vibrations may also be used as an indication of the input rate.

The rate signal produced in either the nulled or nonnulled variations of the restrained pattern modes may be used directly when indications of angular rate are required or may be integrated over periods during which the rate signal is present to indicate the amount of angular input rotation. However, the present invention, by allowing the vibration pattern to rotate freely about azimuth, allows the angular displacement to be determined directly by determining the instantaneous angular position of standing wave pattern with sensors. Working backwards from this angular position, angular rate may then be determined by differentiating the angular position through a computer or differentiating circuit.

In its preferred form, the present invention includes a high-Q bell-like member supported on a base platform by a post. The bell member has sides flaring arcuately outwards and downwards along its polar axis over the post and terminating adjacent the platform in an annular lip. This lip is capable of sustaining a vibration pattern therein and defining nodal and anti-nodal regions spaced alternately and equiangularly thereabout. Telescoped by the bell-like member and supported within the mouth thereof by the platform and post adjacent to the periphery of the sides are two circular electrodes mounted in tandem along the axis of the post. Four other electrodes are affixed to a housing platform that telescopes the bell, circular electrodes, and post is adjustable in azimuth with respect to the base platform while the enclosure defined therebetween is under vacuum.

Electronics connected with one of the circular electrodes provide an energizing potential thereto of suitable frequency, magnitude, and phase to modulate the effective spring constant of the bell sides so as to overcome damping. Moreover, being circular and adjacent the periphery of the bell lip, the forcer electrode is operative to impart energy of the required phase and frequency to at least one anti-nodal region of the rotatable vibration pattern regardless of the azimuth position of the pattern with respect to the input axis. The frequency of the excitation applied to and imparted by the circular forcer is twice the natural frequency of the bell member and therefore corresponds with twice the frequency of the resulting vibration pattern. By this modulating a parameter of the high-Q system at twice the natural frequency of the system to overcome the damping thereon, the excitation is what is known as parametric. The amplitude of this parametrically excited vibration is detected by the sides in relation to the resulting rotation of the flexing second of the tandem circular electrodes at an antinodal region and is utilized to develop feedback signals to the first circular electrode whereby substantially constant amplitude and natural frequency radial vibrations are effected in the bell sides, such vibrations defining the pattern comprising nodal and anti-nodal regions spaced alternately and angularly thereabout.

In the absence of platform rotation the vibration pattern thus parametrically excited remains stationary with respect to the input axis and bell referenced radii. However, with rotation about the input axis, the foregoing structure and system allows the vibration pattern to rotate freely about the input axis with an angular displacement proportional to that of the detector. The extent of such rotation of the vibration pattern is detected by the sensors mounted in the housing platform. These housing mounted electrodes are operative in a uniradial sense as compared with the omniazimuthal sense of the circular forcer and sensor and produce output signals at the natural frequency of the bell. The angle of detector displacement is then determined from the product of the amplitude of the vibration pattern times the cosine of twice the displaced angle times the cosine of the exercising frequency.

It is, therefore, a general object of the present invention to provide a high-Q bell-like rotation detector having sides encircling an input axis, where the sides are flexed in a vibration pattern that rotates about the sides in proportion to rotation of the detector about its input axis and where the energy to cause the flexing is imparted repetitively to the sides at regions that rotate with the pattern.

It is a further object to provide a device of the foregoing type wherein the frequency of the excitation applied to the sides of the bell member to cause the vibration pattern therein is substantially double the natural frequency of the bell or therefore the frequency of the pattern.

It is a further object to provide a device of the foregoing type wherein the electrode causing the vibration pattern is operative to exercise the sides of the high-Q member along any position of an anti-nodal axis of the pattern about the input axis.

It is still a further and more specific object of the present invention to provide a device of the foregoing type wherein the repetitive energy is imparted by a continuous circular electrode fixed to the platform supporting high-Q member.

These and other objects of the present invention will become apparent from the following description and claims taken in connection with the accompanying drawings, wherein:

FIG. 1 is a view in perspective partially broken away of a rotation detector made in accordance with the invention and having a continuous circular forcer;

FIG. 2 is a diagrammatic representation of the flexing action exhibited by the sides, such action and the space in which the sides flex being exaggerated for better understanding;

FIG. 2a is a representation of the rotation of the bell pattern of FIG. 2; and

FIG. 3 is a section through the detector showing the electrodes affixed in the base and housing and means in block diagram form whereby the bell-like member may be operated to indicate rotation about theaxis.

DETAILED DESCRIPTION FIGURE 1 As may be seen with reference to FIG. 1, bell B is supported in an inverted position on post 24 upstanding from platform base 10 and is enclosed thereon by platform housing 12.

Bell B is comprised of arcuate sides that depend contiguously and symmetrically from central area 16 about a shaft 20 along the bells polar or input axis ZZ and that terminate in an arcuate lip 14. In order of progression from center region 16, shaft 20 is comprised of a neck portion 22, a hub section 26 having a lower hub surface 28, a relief groove 30, and axially-extending stem 32, and a terminating end 34 having a threaded portion 36 thereon.

Platform base has an outer surface 42 bounded by a floor 44 and a ledge 46. A circuit board 48 is secured to floor 44 by screws 52, and post 24 upstands from ledge 46 along the ZZ axis. Post 24 is comprised of a hub 54 having an upper hub surface 56 and a bore 58 therethrough concentric with the Z2 polar axis. Also concentric therewith and counterbored in bore 58 are seat 60 and side 62. A circular forcer ring 70 having top 72, bottom 74, inner periphery 76, and outer periphery 78 is secured to and isolated from post 24 and ledge 46 by epoxy 50 and a shield disc 80 is similarly secured to and isolated from forcer top 72.

Conductive brass guard cage 82 comprised of a top disc 84, a cylinder 86, and a bottom disc 88 are secured to and isolated from post 24 and shield 80 and a circular sensor electrode 90 is secured to and electrically isolated from cage 82 by epoxy 50 inserted in the 0.01 inch spaces between the various elements as shown. The outer periphery of base 10 at surface 42 as well as the radially-outwardly facing portions of electrode 70, shield 80, guard 82, electrode 90, and epoxy 50 are contoured to provide an arcuate surface 78 to receive the inner surface of bell lip 14in close spaced-relation therefrom upon assembly therewith. Having axiallyopen portions facing radially outwards from the ZZ axis towards lip 14, guards 82 expose just the face 94 of the electrode 90 to just the inner periphery of lip 14 electrode 90 being elsewhere isolated from platform 10 by guard 82.

A hole 96 drilled into electrode 70 through floor 44 is potted with epoxy and then tapped with threads 98 to receive feedthrough connector 102 comprised of a probe 104 supported in an electrically-isolated guard sleeve 106 having threads to mate threads 98. Guard sleeve 106 is threaded into epoxy 50 so that connector probe tip 104 is in pressure contact with electrode 70. Another hole 108 having counterbored seat 109a and side 10% is drilled into electrode 90 through floor 44, electrode 70, shield 80, and guard bottom disc 88, and is similarly potted and tapped with thread 110. A shield sleeve 92 is then secured in hole 108 by epoxy 50 so as to be in contact with seat 109a and side 1091) of hole 108 and with shield disc 80. Feedthrough connector 112 having a probe 114 and a guard sleeve 116 is potted into shield sleeve 92 and engaged with threads 110 so that probe 114 is in pressure contact with electrode 90 and so that connector guard 116 terminates a guard bottom 88 without contacting electrode 90.

Bell B is secured to post 24 and base 10 by means of a nut 38 threaded onto threads 36 of shaft 20 inserted into post bore 58 to urge washer 40 against counterbore seat 60, thereby also urging lower bell hub surface 28 against upper post hub 56. A groove 64 extending about stem 32 of shaft 20 carries an O ring 66 to permit bell B to be adjusted axially and circumferentially with respect to post 24 and axis ZZ.

Housing platform 12 is comprised of an end wall or roof 118 and cylindrical side walls 120. Roof 118 has a central hub 122 and a surface 124 recessed thereabout to receive a circuit board 126 secured thereto by screws 128. Side walls terminate in an edge 130, have a clamping flange 132 on their outer periphery, and on their inner periphery have a counterbored seat 134 and side 136, the latter having 0 ring groove 138 therein. As may be seen more clearly in conjunction with FIG. 3, guard 140 and electrode 142 are secured by 0.01 inch layers of epoxy 50 in space that protrudes axially and equiradially about the ZZ axis into walls 120 from roof 118.

Guard 140 has an axially-open portion facing radially inwards to expose just sensor face 152 to the outer periphery of lip 14 and terminate at end 154. Elsewhere, the guard, electrode, and housing are isolated from each other by epoxy 50. The inner periphery of walls 120 and portions of sleeve 140 and end 154 as well as electrode 142 and epoxy 50 are removed to provide an arcuate surface 156 to receive the outer periphery of bell lip 14 in close spaced relationship therefrom upon assembly. Also, to reduce damping between housing 12 and the outer periphery of lip 14, twelve axial openings 158, P16. 3, protrude into walls 120 equiradial with spaces 150 and terminate short of roof 118. A port 160 coaxial with an opening 158 extends through surface 118 and is sealed by plug 162 after the apparatus has been assembled and evacuated.

A feedthrough connector 164 is screwed into sleeve 140 so that the connector probe tip 166 is in pressure contact with the electrode and the connector guard 168 is in contact with and terminates at the guard sleeve 140 short of the electrode. Signals developed on probe tips 104, 114, and 166 and guards 106, 116, and 168 of connectors 102, 112, and 164 respectively are brought out thereby to circuit board 48 in base 10 and board 126 in housing 12. These circuit boards carry suitable pads for connection with the probes and guards of the connectors and also carry suitable circuit paths and elements for interconnecting the electrodes and operating the rotation detector as to be more fully described below with reference to FIG. 3. Moreover, being electrically-isolated and physically separated by epoxy 50 from housing 12 and the electrodes, the guards around the sensor electrodes are main-tained electrically by these circuits at substantially the same potential as these electrodes to provide a constant capacitance cage thereabout, thereby enhancing the sensitivity of the sensors to radial lip vibrations.

Base platform 10 carrying bell B fastened thereto is assembled and rigidly secured to housing platform 12 by clamp ring 170 having a counterbored seat 172 and side 174. Clamp ring 170 is fastened to housing platform 12 at edge 130 thereof by eight screws 176 threaded into holes 178. As the screws 176 are tightened, counterbored seat 172 of ring 170 urges bottom surface 44 of base platform 10 and ledge 46 towards seat 134 counterbored in the inner periphery of housing side 120, and base surface 42 slides axially along counterbored side 136. Side 136 having a radial gap of 0.0005 inch from surface 42 centers the latter coarsely therewith, fine centering and sealing therebetween being effected by O ring 139 in groove 138.

Prior to the final tightening of screws 176, the atmosphere internal to the cavity about the bell B defined by platforms l and 12 is evacuated as desired to effect a high-Q for bell B and the relative azimuth positions of the bell B, platform base 10, and platform housing 12 are adjusted. Air may thus be withdrawn from housing 12 through port 160 and the atmosphere therein backfilled with another gas such as helium so as to increase the Q of the hell by decreasing air damping. For instance, it has been found that by maintaining the bell vacuum on the order of IO torrs increases the Q of the device fourfold and hence comparably increases the time constant, or ringing time, of oscillations in relation to the energy input per cycle.

The platform structures, electrodes, and especially bell B are made from a high-Q or low-loss material. By high-Q I refer to the ratio of the energy stored in the oscillating system to the energy dissipated in one cycle. Materials that exhibit favorable Qs, elastic limits, and modulus of elasticity, and yet are readily machinable, include aluminum alloys, such as 2024-T4. This alloy has a composition generally of 93.4 percent aluminum, 4.5 percent copper, 1.5 percent magnesium, and 0.6 percent manganese. Also, silicon aluminum bronze or Everdur alloys, having 96 percent copper, 3 percent silicon, and 1 percent manganese or 91 percent copper, 7 percent aluminum and 2 percent silicon have favorable properties.

Thus, bell B shown in FIG. 1, is preferably constructed from 2024-T4 aluminum having a modulus of elasticity E of 10.6 X 10 psi and a Q of 3,000 in air, 3,000 in helium and up to 12,000 in 10' torr vacuum. The inner and outer peripheries of sides 18 both have a mean radius of 1 inch swung at different points along the Z2 axis and vary in thickness in the arcuate region from maximum h, of 0.20 inches in the center region 16 to some finite thickness h in accordance with the formula h h (I cos 0)/ 4, where 0 is the spherical angle subtended from the polar axis through center 16. This thickness contour is believed to provide surfaces of uniform maximum strain when flexed. When assembled to platforms l0 and 12, lip 14 clears the arcuate faces of the sensor and forcer electrodes by nominally 0.005 inch.

The feedthrough connectors 102, 112, and 164 are Microdot connectors DC-05 l007 available from Microdot Incorporated of South Pasedena, California. Potting adhesive or epoxy 50 may, for example, be that known as P38 obtainable from Bacon Industries of Watertown, Massachusetts. This adhesive is an epoxy resin base compound chosen because of the stability of its composition and dimensions with time and temperature and its high dielectric strength. Moreover, such epoxy has high adhesion, low tendency to crack, low coefficient of linear thermal expansion, low creep, and high tensile strength.

GENERAL OPERATION FIG. 2

As may be understood generally with reference to FIG. 2, the operation of bell B requires that sides thereof be exercised or forced radially so as to flex lip 14 between two extreme positions, shown exaggerated by the dotted and dashed lines, about a neutral unflexed circular position, shown by the solid lines. These exercising vibrations establish about the circumference of the lip a standing wave pattern defining nodal re gions of normally quiescent radial vibrations and antinodal regions of normally maximum radial vibrations. The flexing 'of the bell sides is due predominantly to their bending in contrast to extension and compression as would be the case if the sides expanded and contracted uniformly. Moreover, since the energy required to effect bending is significantly less than that to effect extension and compression and since the energy imparted by the forcer is sufficient to effect bending but not extension, the nodal/anti-nodal pattern obtains.

Such flexing is initiated and sustained by an electromechanical self oscillation loop comprised generally of circular forcer 70, circular sensor 90, and feedback means 184 shown schematically adjacent the sides of the bell, the bell in turn being connnected to a source of constant potential. The forcer is energized at a potential varying at twice the natural frequency of the bell to modulate the electrical contribution to the spring constant of the bell introduced by the energy stored in the electrode. As a result lip 14 flexes in a standing wave pattern having an instantaneous set of anti-nodal regions 14a-14e and l4c-l4g, respectively, along each of two mutually perpendicular directions AA-AA and AB--AB radial to the input or polar axis 22 and an instantaneous set of nodal regions 14b-14f and l4d-l4h, respectively, along each of two mutually perpendicular directions NA-NA and NB-NB midway between those associated with the anti-nodes. These sets of nodal and anti-nodal regions rotate about the sides of the lip as the bell is rotated but are stationary with respect to the bell when it is not rotated.

Rotation of this pattern as the instrument rotates may be understood with reference to FIG. 2 and 2a. As shown in FIG. 2, prior to rotation perpendicular axes XX and YY referenced to and rotating with the bell are aligned with anti-nodal axes AA-AA and .ABAB respectively of the pattern. Rotation of the bell in a counterclockwise direction by some angle [-1 displaces the XX and YY axes a similar amount and direction to a new position XX and Y'Y'. In the course of this rotation, the standing wave pattern is also rotated in the same direction, but only at some angle a, where a equals 0.33. Thus, anti-nodal axes AA-AA and AB-- AB are rotated to A'A-A'A' and AB'--A'B' and nodal axes NA-NA and NB-NB are rotated to N'A'-N'A' and N'B'NB'. For example, as shown in FIG. 2a, if the bell is rotated in a counterclockwise sense for 100 (/3), the pattern rotates only 30.0 (0:). Moreover, this pattern rotation is retrograde with respect to the rotated instrument axes but posigrade with respect to the initial (inertial) orientation of the instrument axes.

Deflections of the lip are detected by sensors located adjacent thereto and measuring either the varying capacitance or varying potential therebetween depending on the input impedance of the circuits connected with the sensors. A sensor detects the amplitude of radial vibrations of lip 14 anti-nodes, and electrical feedback means 184 connect antinodal sensor 90 to anti-nodal forcer 70 thereby closing a loop operative to flex the anti-nodal lip regions at constant maximum amplitude. Other sensor means 142 detect those radial lip vibrations due to the motion of the lip associated with the standing wave pattern and the rotation of the wave pattern about the input axis. Sensor 142, moreover, is connected to readout circuit 186 and develops in conjunction therewith signals usable for indicating the amount and direction of bell rotation.

A feature of the nodal and anti-nodal regions of the vibration pattern imparted and maintained by forcer 70 and sensor 90 is that radial vibrations produced along the anti-nodal AA-AA and AB-AB directions cause the bell to produce substantially no radial vibrations along nodal directions NA-NA and NB-NB in the absence of hell rotation. Similarly, radial vibrations imparted along the nodal directions produce substantially no effects along the anti-nodal directions. In terms of the present invention, the vibrations imparted by forcer 70 at an anti-nodal region causes substantially no additional vibration along the nodal axes.

Another feature inherent in the imparted radial vibration pattern is that radial vibrations along any one anti-nodal axis are mathematically and substantially physically identical in magnitude and frequency to those along any other anti-nodal axis even though such axes are physically separated, and radial vibrations along one nodal axis are similarly identical to those along any other nodal axis even though. physically separated. The effect of this feature is that all nodal and anti-nodal axes may be considered as equivalent respectively to just one nodal and one anti-nodal axis. Thus, radial vibrations applied at one anti-nodal region produce substantially identical radial vibrations at the other anti-nodal regions, and radial vibrations to sustain the standing wave may be imparted with equal effect at any anti-nodal region. To be effective to apply forcing potential at lip anti-nodes, forcer 70 may therefore be a continuous element encircling the lip or may be comprised of segments connected to the same source of varying potential and located about the perimeter of the lip 14 so that one segment of the forcer is always opposite one anti-nodal region regardless of pattern orientation.

DESCRIPTION OF OPERATION FIG. 3

The means comprising the self oscillation and readout loops are shown interconnected in block form in FIG. 3 with the bell sides and electrodes shown schematically in plan view using like designations for similar elements in FIG. 1. Thus, forcer electrode 70 and sensor electrode 90 are disposed on base 10 between post 24 and lip 14 as shown, and electrode 142 is mounted in housing 12.

The FIG. 3 self oscillator loop is comprised generally of the anti-nodal regions of the standing wave in lip 14, electrode 90, oscillator pickoff amplifier 200, level detector 202, amplifier 206, filter 208, dc-to-dc converter 210, demodulator 212, multivibrator 214, flip flop 216, oscillator forcer circuit 218, electrode 70, bell B, and its anti-nodal regions. Electrode 70 is the oscillator forcer electrode connected from oscillator forcer circuit 218 and operative to impart radial exercising vibrations to hell B by applying varying attractive electrical potential at the anti-nodal wave regions along an anti-nodal axis normal to the polar or input axis ZZ. Electrode 90 is the oscillator pickoff electrode connected to oscillator pickoff amplifier 200 and operative to detect radial vibrations of hell B by measuring the varying potential of anti-nodal lip regions with respect to electrode 90 along an anti-nodal axis normal to the Z2 axis.

The output of oscillator pickoff amplifier 200 is connected parallely both to level detector 202 and to demodulator 212. A source of adjustable reference potential 204 is also connected to an input terminal of level detector 202, the output of which is connected to dc-to-dc converter 210 through amplifier and compensator 206 and filter 208 to regulate the amplitude of the exercising wave. Demodulator 212 is connnected to multivibrator 214 and therefrom to frequency dividing flip flop 216. Synchronization pulses are provided by frequency dividing flip flop 216 to start up converter 210 and also to operate demodulator 212, oscillator forcer circuits 218, and monostable 232. The output of demodulator 212 regulates the frequency of multivibrator 214 at four times the natural frequency of the bell so that frequency dividing flip flop 216, in turn, slaves converter 210, demodulator 212, forcer circuit 218, and monostable 232 at substantially twice the resonant frequency.

At start-up, the difference in amplitude between reference potential 204 and the signal from amplifier 200 corresponding to the maximum amplitude of lip 14 is of sufficient magnitude and a polarity to cause an output from dc-to-dc converter 210 to oscillator forcer circuit 218. The amplitude and frequency of the varying potential to oscillator forcer electrode and antinodal wave regions therefore tends to increase the amplitude of lip vibrations. As the amplitude of lip vibrations increase, the input to detector 202 increases the difference from that provided by reference 204. The output from level detector 202 to converter 210 consequently increases to ultimately stabilize at a value corresponding to a substantially constant maximum amplitude of lip vibration, such amplitude being adjustable by setting reference potential 204.

Free-running multivibrator 214 is biased at start-up to cause the output from frequency divider 216 to oscillator forcer circuit 218 to be at a frequency less than the twice resonant frequency of lip 14. Thereafter, the bias to multivibrator 214 is adjusted by the output of demodulator 212 to effect a frequency which produces a maximum amplitude at lip 14 for the converter regulated forcing potential. The forcing potential applied by oscillator forcer circuit 218 to electrode 70 is then a substantial dc bias generated from converter 210 modulated by the double frequency pulses generated in response to flip flop 216. The amplitude of these pulses is continuously controlled by converter 210, and the un-linearities in the components regulating it, to maintain the vibration pattern, thus parametrically excited, at constant amplitude.

The readout loop is comprised generally of readout pickoff electrode 142, readout amplifier 220, demodulator 222, phase shifting monostable vibrator 232, frequency dividing flip flop 236, and compensation amplifier 224. The pulses applied to monostable 232 from flip flop 216 are phase shifted by adjustment means 234 and then applied to demodulator 222 after frequency division by flip flop 236. Electrodes 142 and 146 are readout pickoff electrodes connected to readout amplifier 220 and operative to detect radial vibrations of bell B by measuring the varying potential at regions of the lip. The output of readout amplifier 220 is connected to demodulator 222, the output of which after amplification and compensation in amplifier 224 provides a signal 226 proportional to the rotation of bell B about axis of symmetry ZZ.

In the configuration shown in FIG. 3, signal 226 developed by amplifier 224 varies substantially as the cosine of twice the angle through which the pattern has rotated times the product of the maximum flexing amplitude times the cosine of the exercising frequency. The angle through which platform and bell B mounted thereon are rotated during any given period can be determined from signal 226 as for instance by a computer.

The subject invention has application wherever it is desired to detect motion of a structure about an axis. Applications where the device may be used include those to indicate horizontal and vertical directions, to provide a strapped down or gimballed reference platform, to stabilize a structure against external motions, or to navigate a vehicle over desired course. Moreover, having described one embodiment of the present invention it is understood that the specific terms and examples are employed in a descriptive sense and not for the purpose of limitation. It will be obvious to those skilled in the art that modifications and changes may be made without departing from my invention and I, therefore, aim in the appended claims to cover such modifications and changes as fall within the true spirit and scope of my invention.

What I claim as new and desire to secure by letters of patent of the United States is:

l. A device to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q member carried by said platform along said axis and defining a perimeter about said axis,

said member capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; 1

c. a forcer carried by said platform adjacent said perimeter and operative to impart thereto radial forces sustaining said pattern, said forces having a frequency of twice the frequency of said pattern; and

. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.

2. A device to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q member carried by said platform along said axis and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platd. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.

3. A device to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q member carried along said axis by said platform and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern defining a plurality of nodal and antinodal regions spaced alternately about and rotatable on said perimeter when said platform rotates, the rotation of said pattern varying with the rotation of said platform about said axis to indicate said platform rotation;

c. a forcer carried by said platform adjacent said perimeter to impart thereto periodic pulses thereto sustaining said pattern, said pulses having a frequency of twice the frequency of said pattern and said forcer comprising circumferential sections effective to impart said pulses to a one of said anti-nodal regions for substantially all positions of said pattern about said axis; and

d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.

4. A device to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q bell-like member carried along said axis and having sides radially displaceable towards said axis and defining a perimeter thereabout, said sides capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform;

a forcer carried by said platform adjacent said perimeter and operative to impart thereto radial forces sustaining said pattern said forces having a frequency of twice the frequency of said pattern;

and

d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.

5. A device to sense rotation of a platform about a predetermined axis, comprising in combination:

a. a platform;

b. a high-Q bell-like member carried along said axis and having sides radially displaceable towards said axis and defining a perimeter thereabout, said sides capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform;

. A circular forcer carried by said platfonn adjacent to said perimeter and operative to impart thereto radial forces sustaining said pattern said forces having a frequency of twice the frequency of said pattern; and

d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.

6. The device of claim 5, wherein the ratio of rotac. sensing the change in position of said null region tion of said pattern to the rotation of said platform is produced by said vibrations and said rotation of between 0.2 and 0.4. said member.

7. The method of detecting the rotation of a high-Q 8. The method of detecting movement of a high-Q member about a predetermined axis therethrough, said member about a predetermined axis therethrough, said member having a perimeter about said axis capable of od pri ing the steps of:

sustaining natural frequency vibrations radial to said maimaifling Vibrations n Sa d member radial to axis, rotatable thereabout on said perimeter, and hav- 3X15 and defimng a P y of nodal and ing a substantially null region, said method comprising nodal reglons Spaced thereabout, 531d 8 the steps of: 10 capable of rotating in said member about said axis a. applying to said perimeter forces having a frequenwlthfotatlon of szfld 'f about Said axis; and

cy f twice h frequency f the vibrations b. sensing those radial vibrations produced by the efwh b id ib i are i i fects of said maintained vibrations and rotations of b. rotating said vibrations about said axis in propor- 531d F about a a whereby Said rotation tion to the rotation of said member about said axis; of 531d antl'nodal reglo" and a 

1. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q member carried by said platform along said axis and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; c. a forcer carried by said platform adjacent said perimeter and operative to impart thereto radial forces sustaining said pattern, said forces having a frequency of twice the frequency of said pattern; and d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 1. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q member carried by said platform along said axis and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; c. a forcer carried by said platform adjacent said perimeter and operative to impart thereto radial forces sustaining said pattern, said forces having a frequency of twice the frequency of said pattern; and d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 2. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q member carried by said platform along said axis and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; c. an annular forcer carried by said platform adjacent to said perimeter and operative to impart thereto time varying forces radial to said axis and sustaining said pattern; and d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 3. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q member carried along said axis by said platform and defining a perimeter about said axis, said member capable of sustaining therein a vibration pattern defining a plurality of nodal and anti-nodal regions spaced alternately about and rotatable on said perimeter when said platform rotates, the rotation of said pattern varying with the rotation of said platform about said axis to indicate said platform rotation; c. a forcer carried by said platform adjacent said perimeter to impart thereto periodic pulses thereto sustaining said pattern, said pulses having a frequency of twice the frequency of said pattern and said forcer comprising circumferential sections effective to impart said pulses to a one of said anti-nodal regions for substantially all positions of said pattern about said axis; and d. a sensor carried by said platform adjacent said perimeter and operative to measUre radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 4. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q bell-like member carried along said axis and having sides radially displaceable towards said axis and defining a perimeter thereabout, said sides capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; c. a forcer carried by said platform adjacent said perimeter and operative to impart thereto radial forces sustaining said pattern said forces having a frequency of twice the frequency of said pattern; and d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 5. A device to sense rotation of a platform about a predetermined axis, comprising in combination: a. a platform; b. a high-Q bell-like member carried along said axis and having sides radially displaceable towards said axis and defining a perimeter thereabout, said sides capable of sustaining therein a vibration pattern rotatable about said axis when said platform rotates about said axis, the rotation of said pattern varying with the rotation of said platform; c. A circular forcer carried by said platform adjacent to said perimeter and operative to impart thereto radial forces sustaining said pattern said forces having a frequency of twice the frequency of said pattern; and d. a sensor carried by said platform adjacent said perimeter and operative to measure radial vibrations thereof produced by the effects of said pattern and rotation of said platform about said axis.
 6. The device of claim 5, wherein the ratio of rotation of said pattern to the rotation of said platform is between 0.2 and 0.4.
 7. The method of detecting the rotation of a high-Q member about a predetermined axis therethrough, said member having a perimeter about said axis capable of sustaining natural frequency vibrations radial to said axis, rotatable thereabout on said perimeter, and having a substantially null region, said method comprising the steps of: a. applying to said perimeter forces having a frequency of twice the frequency of the vibrations whereby said vibrations are maintained; b. rotating said vibrations about said axis in proportion to the rotation of said member about said axis; and c. sensing the change in position of said null region produced by said vibrations and said rotation of said member. 